Cycles Noise Issue - No matter what I do it won't go away
Let's walk through troubleshooting this, shall we?

Ok, first, where is the noise in the image? You might notice it does not appear in the sunlit areas, just the shadows. So we can eliminate that it is coming from the first hit (camera > surface) or evaluating the brightness of our main sun light. We can also observe it does not appear solely along the edges of shadows, rather it is spread throughout the shaded areas.

The fact that it is spread evenly in the shaded areas but does not appear in the sunlight tells us it is coming from one of the sources of fill light. That could be an additional light source (like a skydome/HDRI or a fill light) or it could be from global illumination. Or perhaps it is a reflection of fill light. How do we find out?

The answer is in the render passes. Over in the layers panel, enable the direct and indirect (don't worry about the color pass) for glossy and diffuse. Which of the 4 passes contains the noise?

Diffuse direct - Your source of noise is the direct light evaluation itself. This usually comes from HDRIs. Make sure the "multiple importance" option is enabled and the resolution is set to the # of pixels on the longer side of your HDRI map. For example, a 2048x1024 HDRI you would use the value 2048. If you are using the branched path tracing integrator, you can increase the world sample value to send more rays towards this problem for each primary sample.

Diffuse indirect - Your source of noise is global illumination/diffuse reflection: light scattering off a surface and illuminating another surface. Check that you do not have surfaces with excessively bright diffuse colors (diffuse color is the surface albedo, it should never be 100%/1.0. Even 90%/0.9 is uncommon, that's why the default is 0.8). Additionally, try disabling caustics in the light paths panel. These are harder to resolve than normal scattered light. Finally, the more diffuse bounces you have, the greater than chance of a ray taking a "funny bounce" and returning an anomalous value. Reduce this under light paths, many scenes the difference for any values over 2 isn't really noticeable unless you compare with a 2-bounce render. If you are using branched path, increase diffuse samples in the render panel to send more rays to this problem

Glossy direct - Your source of noise is reflections hitting varying parts of a textured light. This is more or less the same problem you'd see in the diffuse direct pass. The solution is the same, check MIS is on for the world and set to an appropriate resolution.

Glossy indirect - Your source of noise is reflections of other objects. Blurry reflections mean a ray can take off in a variety of different directions. Depending on which one it picks, it can catch different objects in the reflection. The final blurry reflection is an average of all of these, but until your trace enough rays for the situation to average out, you get noise. Try using the filter glossy option to contain the possible variance(it limits the shininess as a ray bounces more times), and like with diffuse avoid non-emission shaders with extremely bright colors. You can also lower glossy depth under light paths to try and contain the possible results, although can lead to black reflections if set to low. If you are using branched path, increase glossy samples in render settings to send more rays to this problem